The well-known controversy about the (supposed) difference between sentences such as “cuiuslibet hominis asinus currit ”and “asinus cuiuslibet hominis currit ”is delineated and discussed. It is argued that the issue involved is entirely focused on the question whether or not nouns (names), by their own nature (secundum propriam inventionem), refer to existing things alone. The different answers to this problem (by Bacon, William of Sherwood, and others against certain Parisian masters, among others) are placed within the general framework of medieval semantic thought.